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The light clock: Error and implications

Abstract

The light clock (a photon undergoing successive reflections between two particle mirrors a fixed distance apart) has commonly been used as a theoretical confirmation of the special-relativistic slowing of clock rates. In order to obtain that result one must describe the clock photon in a system moving relatively to the clock. However, contradictory frequency transformations for the photon, as observed from the mirrors, are then predicted by relatively moving observers. A correct and consistent analysis utilizes the Lorentz-invariant relative velocity and distance between the mirrors. An invariant time period is also then involved; a parallel is drawn between it and the invariance of cosmic time for internal processes in distant systems. Considering that space-time and momentum-energy are described by conjugate 4-vectors, it is conjectured that a time transformation occurs only in association with a transformation of energy.

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References

  1. 1.

    M. von Laue,Jahrbuch d. Radioactivität u. Elektronik 14, 263 (1917).

  2. 2.

    R. P. Feynman, R. B. Leighton, and Matthew Sands,The Feynman Lectures on Physics (Addison-Wesley, Reading, Mass., 1963), Vol.I, p. 15–6.

  3. 3.

    R. F. Marzke and J. A. Wheeler, inGravitation and Relativity, Hong-Yee Chiu and W. F. Hoffmann, eds. (Benjamin, New York, 1964), pp. 48–62.

  4. 4.

    C. W. Misner, K. S. Thorne, and J. A. Wheeler,Gravitation (Freeman, San Francisco, 1973), Box 16.4.

  5. 5.

    H. C. Ohanian,Gravitation and Spacetime (Norton, New York, 1976), Chapter 5.

  6. 6.

    J. L. Anderson and R. Gautreau,Am. J. Phys. 37, 178 (1969).

  7. 7.

    Alex Harvey,Gen. Rel. Grav. 7, 891 (1976).

  8. 8.

    A. Aurilia and F. Rohrlich,Am. J. Phys. 43, 261 (1975).

  9. 9.

    R. Schlegel,Found. Phys. 7, 245 (1977).

  10. 10.

    R. Hagedorn,Relativistic Kinematics (Benjamin, New York, 1964).

  11. 11.

    A. Einstein,Ann. Phys. (Lpz) 17, 891 (1905), Section 8 [English translation in H. A. Lorentzet al., The Principle of Relativity (Dover, New York), p. 59]; also see H. P. Robertson and T. W. Noonan,Relativity and Cosmology (Saunders, Philadelphia, 1968), p. 82.

  12. 12.

    R. Schlegel,Superposition and Interaction (Univ. of Chicago Press, Chicago, 1980).

  13. 13.

    G. C. McVittie,Fact and Theory in Cosmology (Eyre & Spottiswoode, London, 1961), pp. 90, 105.

  14. 14.

    H. Bondi,Cosmology (Cambridge Univ. Press, Cambridge, 1952), pp. 71–72.

  15. 15.

    R. Schlegel,Found. Phys. 3, 169 (1973).

  16. 16.

    J. S. Hafele and R. E. Keating,Science 177, 168 (1972).

  17. 17.

    R. Schlegel,Am. J. Phys. 42, 183 (1974).

  18. 18.

    R. Schlegel,Nature 242, 180 (1973).

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Schlegel, R. The light clock: Error and implications. Found Phys 10, 345–351 (1980). https://doi.org/10.1007/BF00715077

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Keywords

  • Reflection
  • Relative Velocity
  • Internal Process
  • Frequency Transformation
  • Fixed Distance